If the value of the expression \(\big(a_{b_{2015}} + 3\big)\big(a_{b_{2016}} + 3\big)\) can be expressed as \(p^{b_{q}} \frac{r}{s}\), where \(b_{q}\) is one of the terms in the recurrence relations sequence above and \((p, r)\) and \((r, s)\) are pairwise coprime integers.